Optimization with Uncertainties over Time: Theory and Algorithms

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Typically, optimization deals exclusively with instances of static problems, with few exceptions. Some exceptions include stochastic optimization and on-line optimization models that treat problems with time-varying uncertainties in the objective functions. Stochastic optimization anticipates that these uncertainties occur in a random fashion and on-line optimization allows for objective functions to be drawn from some pre-specified class of functions, again, in an arbitrary fashion. In the existing literature on constrained optimization, there is litte, if any, evidence of optimization theory or algorithms that treat the class of problems where the uncertainties are both in the objective function and the constraint. The goal of this proposal is to bridge this gap. The significance of the proposed research is twofold: (1) It critically expands the domain of optimization to include a new class of problems a with time-varying nature by developing their background theory; (2) It pioneers some new computational models for solving time-varying problems, and especially those currently arising in data classification, signal processing, and network resource allocations.The proposed research has the potential to impact the design and operation of autonomous engineering systems. It also has the potential to make contribution to the study of information processing systems that support human-centric operations and decisions. Some of the engineered systems that could benefit include: surveillance and monitory systems for tracking environmental and other changes, data management systems (including data analysis, information retrieval, decision support), and wireless communication systems, e.g. mobile phone networks. The proposed research could increase the stability, reliability, and the performance of these systems.